`A = {(1,2,3,......10}` The relation R defined in the set A as R ` = {(x,y) : y = 2x}` . Show that R is not an equivalence relation.

The relation R difined the set Z as R = {(x,y) : x - yin Z} show that R is an equivalence relation.

R is relation in N xxN as (a,b) R (c,d) hArr ad = bc . Show that R is an equivalence relation.

Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L_(1),L_2} : L_(1) is parallel to L_2 } . Show that R is an equivalence relation . Find the set of all lines related to the line y = 2x + 4.

Show that the relation R in the set Z of intergers given by R ={(a,b):2 divides a-b } is an equivalence relation.

Show that the relation R defined by (a,b) R (c,d) implies a + d = b +c on the set N xxN is an equivalence relation.

The relation R is defined on the set of natural numbers as {(a,b): a = 2b}, the R^(-1) is given by

Show that the relation R defined in the set A of all triangles as R = {(T_(1),T_(2)}T_(1) is similar to T_2 } , is equivalence relation . Consider three right angle triangles T_1 with sides 3,4,5 , T_2 with sides 5,12, 13 and T_3 with sides 6, 8, 10 . Which triangles among T_1 , T_2 and T_3 are related ?

Show that the relation R defined in the set A of all polygons as R = {(P_(1),P_2):P_1 and P_2 have same number of sides} , is an equivalence relation . What is the set of all elements in A related to the right angle triangle T with sides 3,4 and 5 ?